# Hypothesis testing with poisson distribution

At a nuclear plant great care is taken to measure the employees health.These are the number of visits made by each of the 10 employees to the doctor during a calender year. 3,6,5,7,4,2,3,5,1,4

Assuming the number of visits made by employee has a poisson distribution ,test the hypothesis that the annual mean per employee is greater than 3.

I am using the graphical method and I am not sure of which p[X=x] should i consider.

X: no.of visits by each employee to the doctor.

H0:$\lambda$=3
H1:$\lambda$>3
X follows a Poisson(3)


Then what is the probability that I should check?

What I did was as the average of sample data is 4,calculated p[X=4] and checked if it was in the critical region. Is this the correct probability to calculate?

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